Welfare Analysis -- First Order Approximation of Equilibrium Conditions and Second Order Approximation of Welfare

[jpfeifer]

Can we do welfare analysis after log_linearizing?

The general answer is no, you cannot do this. Due to certainty equivalence, stochastics will not affect the welfare ranking. In some cases, you can do a naive linear-quadratic approach, but generally, full second order is required. See Woodford (2002): “Inflation Stabilization and Welfare” for a thorough discussion

Why do you want a first order approximation instead of a proper second order one? And why do you want to compute unconditional welfare and the consumption equivalent based on simulated moments?

You may want to look at DSGE_mod/Born_Pfeifer_2018/Welfare at master · JohannesPfeifer/DSGE_mod · GitHub